Please check Settings > Privacy & Security > Speech Recognition on your device's Settings app to ensure that Just Press Record is enabled.
If there is no Just Press Record entry there, check that you have no restrictions set in Settings > Screen Time > Content & Privacy Restrictions > Speech Recognition.
If that doesn’t help, try deleting Just Press Record then restarting your device before re-installing Just Press Record from your past purchases on the App Store.
If that doesn’t help, you can reset your device’s Privacy settings in Settings > General > Transfer or Reset > Reset Location and Privacy.** Please note - if you have used Just Press Record's Local Storage option (instead of iCloud Drive), deleting the app from your iPad will also delete your recordings. However, if your recordings are stored in iCloud Drive, they will not be delete along with the app **